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Simplifying x2 + -51x + -630 = 0 Reorder the terms: -630 + -51x + x2 = 0 Solving -630 + -51x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '630' to each side of the equation. -630 + -51x + 630 + x2 = 0 + 630 Reorder the terms: -630 + 630 + -51x + x2 = 0 + 630 Combine like terms: -630 + 630 = 0 0 + -51x + x2 = 0 + 630 -51x + x2 = 0 + 630 Combine like terms: 0 + 630 = 630 -51x + x2 = 630 The x term is -51x. Take half its coefficient (-25.5). Square it (650.25) and add it to both sides. Add '650.25' to each side of the equation. -51x + 650.25 + x2 = 630 + 650.25 Reorder the terms: 650.25 + -51x + x2 = 630 + 650.25 Combine like terms: 630 + 650.25 = 1280.25 650.25 + -51x + x2 = 1280.25 Factor a perfect square on the left side: (x + -25.5)(x + -25.5) = 1280.25 Calculate the square root of the right side: 35.780581326 Break this problem into two subproblems by setting (x + -25.5) equal to 35.780581326 and -35.780581326.Subproblem 1
x + -25.5 = 35.780581326 Simplifying x + -25.5 = 35.780581326 Reorder the terms: -25.5 + x = 35.780581326 Solving -25.5 + x = 35.780581326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.5' to each side of the equation. -25.5 + 25.5 + x = 35.780581326 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + x = 35.780581326 + 25.5 x = 35.780581326 + 25.5 Combine like terms: 35.780581326 + 25.5 = 61.280581326 x = 61.280581326 Simplifying x = 61.280581326Subproblem 2
x + -25.5 = -35.780581326 Simplifying x + -25.5 = -35.780581326 Reorder the terms: -25.5 + x = -35.780581326 Solving -25.5 + x = -35.780581326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.5' to each side of the equation. -25.5 + 25.5 + x = -35.780581326 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + x = -35.780581326 + 25.5 x = -35.780581326 + 25.5 Combine like terms: -35.780581326 + 25.5 = -10.280581326 x = -10.280581326 Simplifying x = -10.280581326Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.280581326, -10.280581326}
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